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Mon Sep 18, 2017 The Cabot Projection

I've added a new projection to… No, sorry, I added a very old projection. It is the Cabot projection created in 1544 by Sebastian Cabot, son of the Venetian explorer Giovanni Caboto (engl. John Cabot).

And that’s pretty much all I know about this projection. I could add thatit has an aspect ratio of 1:1.33, which is is rarely seen these days. But above all, that I like it quite well! I like its peculiar shape.

What I don’t like so much is the aspect ratio and the resulting vertical stretch of the middle latitudes. Fortunately, both shortcomings can be resolved by a simple modification: I have simply stretched the projection horizontally, and after a few attempts I decided to use a factor of 1.35, which corresponds to an aspect ratio of about 1:1.8. The equatorial regions are still stretched a little bit, but on the whole this result seemed more beautiful than, for example, at a ratio of 1:2.

And although the world certainly doesn’t need any further pseudocylindrical projections, I couldn’t resist the temptation to add this modification to the website as well. Of course I would have liked to call this variant Cabot-Jung… ;-)
But honestly, in my opinion a simple stretch doesn’t reach the necessary threshold of originality to give the design my own name. So it is simply listed under the name Cabot modified.

Finally, I would like to present a reproduction of the original map of 1544. Interestingly, it is stretched vertically even more, its aspect ratio is about 1:1.27 – no idea how to explain it.

cc by nc sa Licensed under CC BY-NC-SA.
Map reproduction courtesy of the Norman B. Leventhal Map Center at the Boston Public Library [ Source ]


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Peter Denner

Do you know how it's constructed? It looks very similar to Eckert III and Winkel II. Could it also be the average of Apian II and the equirectangular projection, just with a higher standard parallel for the equirectangular projection? If so, that would probably make it the earliest known instance of deriving a new projection from an existing parent projection.

A standard parallel of 75 degrees for the equirectangular projection would give an aspect ratio of 1.26, so that could be where the approximately 1.27 comes from.
Thu Feb 02, 2023 4:08 pm CET   –    4 replies

Tobias Jung

Hi Peter,

I don’t know how it’s constructed. Using the average of Apian II and the equirectangular projection, I couldn’t get an exact match so far, but it’s really close. Well spotted! :-)
Thu Feb 02, 2023 5:13 pm CET

Peter Denner

If you're comparing with the 4:3 aspect ratio version, then you'd need a standard parallel of arccos(1/3) = 70.53 degrees.
Thu Feb 02, 2023 7:14 pm CET

Tobias Jung

Yes! That’s it. :-)
They match exactly.
Thu Feb 02, 2023 7:44 pm CET

Peter Denner

Excellent! Now the question is whether the version that's even more vertically stretched has a standard parallel of 75 degrees or so, or whether it's also calculated with a standard parallel of 70.53 degrees and then stretched. The pole line length would be different in each case.
Sat Feb 11, 2023 7:22 am CET
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